Control of Dynamic Systems Using Bayesian Networks RAINER DEVENTER,J OACHIM DENZLER,HEINRICH NIEMANN Chair for pattern recognition Martensstr. 3 D 91058 Erlangen Telephone: +49 (0)9131 85-27825 deventer, denzler, niemann @informatik.uni-erlangen.de Abstract. Bayesian networks for the static as well as for the dynamic case have gained an enormous interest in the research community of artificial intelligence, machine learning and pattern recognition. Although the parallels between dynamic Bayesian networks and Kalman filters are well known since many years, Bayesian networks have not been applied to problems in the area of adaptive control of dynamic systems. In our work we exploit the well know similarities between Bayesian networks and Kalman filters to model and control linear dynamic systems using dynamic Bayesian networks. We show, how the model is used to calculate appropriate input signals for the dynamic system to achieve a required output signal. First the desired output value is entered as additional evidence. Then marginalization results in the most likely values of the input nodes. The experiments show that with our approach the desired value is reached in reasonable time and with great accuracy. Additionally, oscillating systems can be handled. The benefits of the proposed approach are the model based control strategy and the possibility to learn the structure and probabilities of the Bayesian network from examples. Keywords: Dynamic Bayesian Networks, Kalman filter, Dynamic System, Controller 1 Introduction Bayesian networks (BN) for the static as well as for the dynamic case have gained an enormous interest in the re- search community of artificial intelligence, machine learn- ing and pattern recognition. Recently, BN have been ap- plied also to static problems in production, since produc- tion processes become more and more complex so that an- alytical modeling and manual design are too expensive. One example for the successful application of BN to a static system in production are the quality evaluation and process parameter selection in order to reach an acceptable quality level [3]. Although the parallels between BN and Kalman fil- ters are well known since many years, BN have not been applied to problems in the area of adaptive control of dy- namic systems. Adaptive control of dynamic systems is one major problem in production processes. Compared to classical control methods BN have the advantage that the model (of the static or dynamic system) can be trained from examples if the model is not available in analytical form. During training missing information can be handled This work was funded by the ,,Deutsche Forschungsgemein- schaft” (DFG) under grant number SFB 396, project-part C1 which makes BN superior to other self adaptive systems like artificial neural networks. Finally, BN can also solve inverse problems, i.e. in any case the most likely param- eters of the system can be computed given information about some parameters of the system that is entered as ev- idence in the BN. In this paper it is shown that BN can also act as con- troller. We exploit the well know similarities between BN and Kalman filters to model and control linear dynamic systems using dynamic Bayesian networks (DBN). We show, how the model is used to calculate appropriate input signals for the dynamic system to achieve a required out- put signal. The desired value is entered as evidence, then, marginalization results in the most likely values of the in- put nodes. Additionally, any other parameter of the dy- namic system can be inferred given the remaining param- eters as evidence. This procedure together with the well known training algorithms for BNs allows the realization of self adaptive controllers which is particularly important for nonlinear processes. We focus in the paper on the modeling of stationary, linear dynamic systems of second order. The extension to control nonlinear systems, though, is straight forward us- ing hybrid BN, i. e. a BN using both discrete and continu-